Using the Wikipedia article as source, lances were indeed once-use items for shock attacks. If they hadn't splintered then they were sure to have gotten stuck, so they were intended to be dropped.
This is with the heavy lances most people seem to have in mind, when they think of a charge by heavily armoured knights.
However, anecdotal, I'm friends with people who are into reenactment of mounted medieval warfare. Mostly mounted archery, but they also practise with lances. Using the lighter and shorter lances used both before and after the era of the heavy knight, they practise "pokey pokey stab stab" while both holding on to the weapon, removing it from the target it got stuck in, getting it back into position to stick it into a new target. All this in full gallop or at least fast trot.
The idea is to be able to hold the lance firmly in the moment of stabby-stab and then loosen the grip allowing the hand to slide along the shaft while riding over the target. Once past, with an again-tightened grip, you use momentum to pull the lance with you and out of the target.
There's likely to be videos out there, but I'm only familiar with some of the ones they have on their Facebook group and from watching them during practise.
Edit: to integrate some of the comments
It should also be noted that, contrary to our image of the charging and heavily armoured knight (and horse) with long lances braced against the rider, this was only a late medi-eval development.
Especially before the introduction of the stirrup, using shorter lances for throwing and over-arm stabbing - as used by Persian, Median or Gothic tribes - would have been not just more common, but rather the only way to exert thrust without Newton teaching you a lesson in physics.
The stirrup changed much: it allowed knights to brace themselves for maximum forward thrust, it allowed mounted archers to stand in them to stabilise their aim.
In all cases, the best horse warriors came from cultures in which it was trained "from birth". Even the Romans always remained an infantry: cavalry came from the Alae - the cultures allied with them. Any attempt by a non-equestrian to ride a horse in battle would end quickly and tragically. In fact, not even riding in battle would quite possibly end tragically, for horse and rider.